Density Weighted Twin Support Vector Machines for Binary Class Imbalance Learning

Usually the real-world (RW) datasets are imbalanced in nature, i.e., there is a significant difference between the number of negative and positive class samples in the datasets. Because of this, most of the conventional classifiers do not perform well on RW data classification problems. To handle the class imbalanced problems in RW datasets, this paper presents a novel density-weighted twin support vector machine (DWTWSVM) for binary class imbalance learning (CIL). Further, to boost the computational speed of DWTWSVM, a density-weighted least squares twin support vector machine (DWLSTSVM) is also proposed for solving the CIL problem, where, the optimization problem is solved by simply considering the equality constraints and by considering the 2-norm of slack variables. The key ideas behind the models are that during the model training phase, the training data points are given weights based on their importance, i.e., the majority class samples are given more importance compared to the minority class samples. Simulations are carried on a synthetic imbalanced and some real-world imbalanced datasets. The model performance in terms of F₁-score, G-mean, recall and precision of the proposed DWTWSVM and DWLSTSVM are compared with support vector machine (SVM), twin SVM (TWSVM), least squares TWSVM (LSTWSVM), fuzzy TWSVM (FTWSVM), improved fuzzy least squares TWSVM (IFLSTWSVM) and density-weighted SVM for binary CIL. Finally, a statistical study is carried out based on F₁-score and G-mean on RW datasets to verify the efficacy and usability of the suggested models.